R: The Zipf Distribution

Zipf {VGAM}

R Documentation

The Zipf Distribution

Description

Density, and cumulative distribution function for the Zipf distribution.

Usage

dzipf(x, N, s, log = FALSE)
pzipf(q, N, s, log.p = FALSE)

Arguments

x, q

vector of quantiles.

`N, s`	the number of elements, and the exponent characterizing the distribution. See `zipf` for more details.
`log`	Logical. If `log = TRUE` then the logarithm of the density is returned.
`log.p`	Same meaning as in `pnorm` or `qnorm`.

Details

This is a finite version of the zeta distribution. See zipf for more details.

Value

dzipf gives the density, and pzipf gives the cumulative distribution function.

Author(s)

T. W. Yee

Examples

N <- 10; s <- 0.5; y <- 1:N
proby <- dzipf(y, N = N, s = s)
## Not run:  plot(proby ~ y, type = "h", col = "blue", ylab = "Probability",
     ylim = c(0, 0.2), main = paste("Zipf(N = ",N,", s = ",s,")", sep = ""),
     lwd = 2, las = 1) 
## End(Not run)
sum(proby)  # Should be 1
max(abs(cumsum(proby) - pzipf(y, N = N, s = s)))  # Should be 0

[Package VGAM version 1.0-1 Index]